Learn the definition of variable and expression and how to simplify variable expressions.

## Related Topics

- How to Translate Phrases into an Algebraic Statement
- How to Simplify Polynomial Expressions
- How to Use the Distributive Property
- How to Evaluate One Variable
- How to Evaluate Two Variables

## Step by step guide to simplifying variable expressions

- In algebra, a variable is a letter used to stand for a number. The most common letters are: \(x, y, z, a, b, c, m\) and \(n\).
- An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
- In an expression, we can combine “
**like**” terms. (values with same variable and same power)

### Simplifying Variable Expressions – Example 1:

Simplify this expression. \(2 \ x \ + \ 3 \ x \ + \ 4=\)?

**Solution:**

Combine “**like**” terms. Then: \(2 \ x \ + \ 3 \ x \ = 5 \ x \) (remember you cannot combine variables and numbers).

Then: \(2 \ x \ + \ 3 \ x \ + \ 4=5 \ x \ + \ 4\) (remember you cannot combine variables and numbers).

### Simplifying Variable Expressions – Example 2:

Simplify this expression. \(12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}=\)?

**Solution:**

Combine “**like**” terms. \(- \ 3 \ x^{2} \ + \ 4 \ x^{2}=x^{2}\)

Then: \(12 \ – \ 3 \ x^{2} \ + \ 5 \ x \ + \ 4 \ x^{2}\) \(=12 \ + \ x^2 \ + \ 5 \ x\). Write in standard form (biggest powers first): \(x^2 \ + \ 5 \ x \ + \ 12\)

### Simplifying Variable Expressions – Example 3:

Simplify this expression. \((10x+2x+3)=\)?

**Solution:**

Combine “**like**” terms. Then: \((10x+2x+3)=12x+3\) (remember you cannot combine variables and numbers).

### Simplifying Variable Expressions – Example 4:

Simplify this expression. \(12-3x^2+9x+5x^2=\)?

**Solution:**

Combine “**like**” terms: \(-3x^2+5x^2=2x^2\)

Then: \(12-3x^2+9x+5x^2=12+2x^2+9x\). Write in standard form (biggest powers first): \(2x^2+9x+12\)

## Exercises for Simplifying Variable Expressions

### Simplify each expression.

- \(\color{blue}{– 2 – x^2 – 6x^2}\)
- \(\color{blue}{ 3 + 10x^2 + 2}\)
- \(\color{blue}{ 8x^2 + 6x + 7x^2}\)
- \(\color{blue}{5x^2 – 12x^2 + 8x }\)
- \(\color{blue}{– 2(4 – 6x) – 3x }\)
- \(\color{blue}{ 9 – 2x + 5x + 2}\)

### Download Simplifying Variable Expressions Worksheet

## Answers

- \(\color{blue}{– 7x^2 – 2}\)
- \(\color{blue}{10x^2 + 5}\)
- \(\color{blue}{15x^2 + 6x}\)
- \(\color{blue}{– 7x^2 + 8x}\)
- \(\color{blue}{9x \ – 8 }\)
- \(\color{blue}{3x \ + 11}\)

I don’t think this site is effortless. It’s effortful!

Thank you for your feedback Elena! We are constantly working on our website to improve its quality. If you have any suggestions please let us know.

I have already shared this site with parents of my tutoring students. Parents are always looking for good suggestions and your other materials for purchase look very nice, too. I’m looking forward to helping my students as we work through this prealgebra material, together. I’ll make sure I share the actual links with my students and not pictures of the worksheets!

Thank you Denise for using our math resources!